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On the existence of bi--pyramidal central configurations of the $n+2$--body problem with an $n$--gon base
Boundary values of the resolvent of Schrödinger hamiltonians with potentials of order zero
1. | Departamento de Ciencias Básicas, UAM-A, Av. San Pablo 180, Col. Reynosa, México D.F. 02200, Mexico |
References:
[1] |
S. Agmon, Spectral properties of Schrödinger operators and scattering theory, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 2 (1975), 151-218. |
[2] |
S. Agmon, J. Cruz and I. Herbst, Generalized Fourier transform for Schrödinger operators with potentials of order zero, Journal of Functional Analysis, 167 (1999), 345-369.
doi: 10.1006/jfan.1999.3432. |
[3] |
S. Agmon and L. Hörmander, Asymptotic properties of solutions of differential equations with simple characteristics, Journal D'Analyse Mathématique, 30 (1976), 1–-38. |
[4] |
G. Barles, On eikonal equations associated with Schrödinger operators with nonspherical radiation conditions, Commun. in Partial Differential Equations, 12 (1987), 263-283. |
[5] |
J. Cruz-Sampedro, The eikonal equation and a class of Schrödinger-like operators, Submitted 2011. |
[6] |
J. Dereziński and C. Gérard, "Scattering Theory of Classical and Quantum $N$-Particle Systems," Springer, 1997. |
[7] |
W. Jäger, Über das Dirichletsche Auβenraumproblem fü die Schwingungsgleichung, Math. Zeitschr, 95 (1967), 299-323.
doi: 10.1007/BF01111082. |
[8] |
A. Jensen and P. Perry, Commutator methods and Besov space estimates for Schrödinger operators, J. Operator Theory, 14 (1985), 181-188. |
[9] |
D. Jerison and C. Kenig, Unique continuation and absence of positive eigenvalues for Schrödinger operators, Ann. Math., 121 (1985), 463-494.
doi: 10.2307/1971205. |
[10] |
E. Mourre, Absence of singular continuous spectrum for certain self-adjoint operators, Commun. Math. Phys., 78 (1980/81), 391-408.
doi: 10.1007/BF01942331. |
[11] |
P. Perry, I. Sigal and B. Simon, Spectral analysis of $N$-body Schrödinger operators, Ann. Math., 114 (1981), 519-567.
doi: 10.2307/1971301. |
[12] |
M. Reed and B. Simon, "Methods of Modern Mathematical Physics, III Sacattering Theory," New York, Academic Press, 1979. |
[13] |
M. Reed and B. Simon, "Methods of Modern Mathematical Physics, IV Analysis of Operators," Academic Press, 1978. |
[14] |
Y. Saitō, Schrödinger operators with a nonspherical radiation condition, Pacific Journal of Mathematics, 126 (1987), 331-359. |
[15] |
I. Sigal, "Scattering Theory for Many-Body Quantum Mechanical Systems," Lecture Notes in Mathematics 1011, Springer Verlag 1983. |
[16] |
G. Stampacchia, Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus, (French) Ann. Inst. Fourier (Grenoble), 15 (1965), 189-258. |
show all references
References:
[1] |
S. Agmon, Spectral properties of Schrödinger operators and scattering theory, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 2 (1975), 151-218. |
[2] |
S. Agmon, J. Cruz and I. Herbst, Generalized Fourier transform for Schrödinger operators with potentials of order zero, Journal of Functional Analysis, 167 (1999), 345-369.
doi: 10.1006/jfan.1999.3432. |
[3] |
S. Agmon and L. Hörmander, Asymptotic properties of solutions of differential equations with simple characteristics, Journal D'Analyse Mathématique, 30 (1976), 1–-38. |
[4] |
G. Barles, On eikonal equations associated with Schrödinger operators with nonspherical radiation conditions, Commun. in Partial Differential Equations, 12 (1987), 263-283. |
[5] |
J. Cruz-Sampedro, The eikonal equation and a class of Schrödinger-like operators, Submitted 2011. |
[6] |
J. Dereziński and C. Gérard, "Scattering Theory of Classical and Quantum $N$-Particle Systems," Springer, 1997. |
[7] |
W. Jäger, Über das Dirichletsche Auβenraumproblem fü die Schwingungsgleichung, Math. Zeitschr, 95 (1967), 299-323.
doi: 10.1007/BF01111082. |
[8] |
A. Jensen and P. Perry, Commutator methods and Besov space estimates for Schrödinger operators, J. Operator Theory, 14 (1985), 181-188. |
[9] |
D. Jerison and C. Kenig, Unique continuation and absence of positive eigenvalues for Schrödinger operators, Ann. Math., 121 (1985), 463-494.
doi: 10.2307/1971205. |
[10] |
E. Mourre, Absence of singular continuous spectrum for certain self-adjoint operators, Commun. Math. Phys., 78 (1980/81), 391-408.
doi: 10.1007/BF01942331. |
[11] |
P. Perry, I. Sigal and B. Simon, Spectral analysis of $N$-body Schrödinger operators, Ann. Math., 114 (1981), 519-567.
doi: 10.2307/1971301. |
[12] |
M. Reed and B. Simon, "Methods of Modern Mathematical Physics, III Sacattering Theory," New York, Academic Press, 1979. |
[13] |
M. Reed and B. Simon, "Methods of Modern Mathematical Physics, IV Analysis of Operators," Academic Press, 1978. |
[14] |
Y. Saitō, Schrödinger operators with a nonspherical radiation condition, Pacific Journal of Mathematics, 126 (1987), 331-359. |
[15] |
I. Sigal, "Scattering Theory for Many-Body Quantum Mechanical Systems," Lecture Notes in Mathematics 1011, Springer Verlag 1983. |
[16] |
G. Stampacchia, Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus, (French) Ann. Inst. Fourier (Grenoble), 15 (1965), 189-258. |
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